Question

With what speed the earth may rotate so that the bodies lying at equator may fly off

Answer 1

For that we Need the inward force pulling the body toward Earth to be equal to outward centrifugal force so that they may just fly off
inward force is mg ,
mg = momega² *R
so g= omega² * R
So it's angular Velocity should be √(g/R)
outward force can also be written as
mg = mv²/R ( as v= Omega*R)
v= √Rg
This v is the linear Velocity of Earth and Omega is angular velocity which means the angle displace in unit time

Hope it Helps ,